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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
MCQ
If a matrix $A=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]$, then the matrix $A A^{\prime}$ (where $A^{\prime}$ is the transpose of $A$ ) is
  • A
    14
  • B
    $\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3\end{array}\right]$
  • C
    $\left[\begin{array}{lll}1 & 2 & 3 \\ 2 & 3 & 1 \\ 3 & 1 & 2\end{array}\right]$
  • D
    [14]
✓

Answer

$(d): A=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]$
$A^{\prime}=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]$
So, $A A^{\prime}=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]=[1+4+9]=[14]$

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